Two blocks, A and B, of mass m and 3m respectively, are connected through a cable and a pulley (see figure 3.1). Block A is also attached to a spring, which is fixed to the ground and has a spring constant k = 50 N/m. Block B is on an inclined plane forming an angle of 30 degrees with the horizontal line. Block B is released from rest with no slack in the cable and with the spring not being stretched or compressed. Assign to m the value in kg of your body weight, then (a) calculate the distance covered by block B once it stops for the first time; assume that there is no friction. (b) assume a kinetic friction force F = 5 N acts on block B and calculate the distance covered by block B once it stops for the first time. State any assumptions and comment on your solutions. B 3m 30° m 112

Two blocks, A and B, of mass m and 3m respectively, are connected through a cable and a pulley (see figure 3.1). Block A is also attached to a spring, which is fixed to the ground and has a spring constant k = 50 N/m. Block B is on an inclined plane forming an angle of 30 degrees with the horizontal line. Block B is released from rest with no slack in the cable and with the spring not being stretched or compressed. Assign to m the value in kg of your body weight, then (a) calculate the distance covered by block B once it stops for the first time; assume that there is no friction. (b) assume a kinetic friction force F = 5 N acts on block B and calculate the distance covered by block B once it stops for the first time. State any assumptions and comment on your solutions. B 3m 30° m 112

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter5: Newton's Laws Of Motion

Section: Chapter Questions

Problem 44PQ: A student working on a school project modeled a trampoline as a spring obeying Hookes law and...

See similar textbooks

Similar questions

An athlete jumping vertically on a trampoline leaves the surface with a velocity of 8.5 m/s upward. What maximum height does she reach? (a) 13 m (b) 2.3 m (c) 3.7 m (d) 0.27 m (e) The answer cant be determined because the mass of the athlete isnt given.
A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using an air track, a stopwatch, and a meterstick. The top of the track is measured to be 1.774 cm higher than the bottom of the track, and the length of the track is d = 127.1 cm. The cart is released from rest at the top of the incline, taken as x = 0, and its position x along the incline is measured as a function of time. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively. (a) Construct a graph of x versus t2, with a best-fit straight line to describe the data. (b) Determine the acceleration of the cart from the slope of this graph. (c) Explain how your answer to part (b) compares with the theoretical value you calculate using a = g sin as derived in Example 4.3.
A particle moves in a medium under the influence of a retarding force equal to mk(υ3+ a2υ), where k and a are constants. Show that for any value of the initial speed the particle will never move a distance greater than π/2kaand that the particle comes to rest only for t → ∞.
When a body slides down an inclined plane, does the work of friction depend on the body’s initial speed? Answer the same question for a body sliding down a curved surface.
You are lying in your bedroom, resting after doing your physics homework. As you stare at your ceiling, you come up with the idea for a new game. You grab a dart with a sticky nose and a mass of 19.0 g. You also grab a spring that has been lying on your desk from some previous project. You paint a target pattern on your ceiling. Your new game is to place the spring vertically on the floor, place the sticky-nose dart facing upward on the spring, and push the spring downward until the coils all press together, as on the right in Figure P7.26. You will then release the spring, firing the dart up toward the target on your ceiling, where its sticky nose will make it hang from the ceiling. The spring has an uncompressed end-to-end length of 5.00 cm, as shown on the left in Figure P7.26, and can be compressed to an end-to-end length of 1.00 cm when the coils are all pressed together. Before trying the game, you hold the upper end of the spring in one hand and hang a bundle of ten identical darts from the lower end of the spring. The spring extends by 1.00 cm due to the weight of the darts. You are so excited about the new game that, before doing a test of the game, you run out to gather your friends to show them. When your friends are in your room watching and you show them the first firing of your new game, why are you embarrassed?
A dart is inserted into a spring-loaded dart gun by pushing the spring in by a distance x. For the next loading, the spring is compressed a distance 2x. How much faster does the second dart leave the gun compared with the first? (a) four times as fast (b) two times as fast (c) the same (d) half as fast (e) one-fourth as fast
A 1.00-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P7.68a). The object has a speed of vi = 3.00 m/s when it makes contact with a light spring (Fig. P7.68b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Fig. P7.68c). The object is then forced toward the left by the spring (Fig. P7.68d) and continues to move in that direction beyond the springs unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Fig. P7.68e). Find (a) the distance of compression d, (b) the speed v at the unstretched position when the object is moving to the left (Fig. P7.68d), and (c) the distance D where the object comes to rest. Figure P7.68
Why is the following situation impossible? In a new casino, a supersized pinball machine is introduced. Casino advertising boasts that a professional basketball player can lie on top of the machine and his head and feet will not hang off the edge! The ball launcher in the machine sends metal balls up one side of the machine and then into play. The spring in the launcher (Fig. P6.60) has a force constant of 1.20 N/cm. The surface on which the ball moves is inclined = 10.0 with respect to the horizontal. The spring is initially compressed its maximum distance d = 5.00 cm. A ball of mass 100 g is projected into play by releasing the plunger. Casino visitors find the play of the giant machine quite exciting.
If the net work done by external forces on a particle is zero, which of the following statements about the particle must be true? (a) Its velocity is zero. (b) Its velocity is decreased. (c) Its velocity is unchanged. (d) Its speed is unchanged. (e) More information is needed.
A 40.0-kg child swings in a swing supported by two chains, each 3.00 m long. The tension in each chain at the lowest point is 350 N. Find (a) the childs speed at the lowest point and (b) the force exerted by the seat on the child at the lowest point. (Ignore the mass of the seat.)
A block of mass 0.250 kg is placed on top of a light, vertical spring of force constant 5 000 N/m and pushed downward so that the spring is compressed by 0.100 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise?
A pendulum consists of a small object called a bob hanging from a light cord of fixed length, with the top end of the cord fixed, as represented in Figure OQ5.6. The bob moves without friction, swinging equally high on both sides. It moves from its turning point A through point B and reaches its maximum speed at point C. (a) Of these points, is there a point where the bob has nonzero radial acceleration and zero tangential acceleration? If so, which point? What is the direction of its total acceleration at this point? (b) Of these points, is there a point where the bob has nonzero tangential acceleration and zero radial acceleration? If so, which point? What is the direction of its total acceleration at this point? (c) Is there a point where the bob has no acceleration? If so, which point? (d) Is there a point where the bob has both nonzero tangential and radial acceleration? If so, which point? What is the direction of its total acceleration at this point? Figure OQ5.6