A small block of mass m slides without friction down a wedge-shaped block of mass M and of opening angle 0. The triangular block itself slides along a horizontal floor, without friction. Then the DOF and equation of constraint are: M
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- Consider a large truck carrying a heavy load, such as steel beams. A significant hazard for the driver is that the load may slide forward, crushing the cab, if the truck stops suddenly in an accident or even in braking. Assume, for example, that a 10,000 kg load sits on the flat bed of a 15,000 kg truck moving at 13.0 m/s. Assume that the load is not tied down to the truck, but has a coefficient of friction of 0.450 with the flat bed of the truck. (a) Calculate the minimum stopping distance for the truck for which the load will not slide forward relative to the truck. m (b) Is any piece of data unnecessary for the solution? (Select all that apply.) mass of truck speed of truck mass of load coefficient of frictionOn a horizontal plane a block of mass m = 0.30 kg is placed and initially held at rest. To this block a massless string is attached and it initially keeps another block of mass M = 0.50 kg vertically at rest via a fixed pulley as shown in Figure. The coefficient of kinetic friction between the block m and the plane is Pk -0.25, but the friction between the block M and the vertical wall is zero. Calculate the tension T by string in N. (Hint: First calculate the acceleration of m or M. And set up the equation of motion for M to find the tension T.) T m MA two mass system is shown below. The block m1, 10 kg, sits on a 30 degree incline with a coefficient µs = 0.6 between the block and the incline. A mass m2 is attached to mi by a frictionless pulley system and the two blocks are released from rest. (a) Draw and label the free body diagram for the m1 block while it is moving on the ramp: Iml 30° (b) How much mass m2 is needed to pull the 10 kg block, m1, up the ramp? (c) If m2 = 15 kg, how long does it take the block to travel a distance 5m on the incline surface? Let uk = 0.3.
- Problems 1. Three forces act on particle A located at the origin of an x-y coordinate system. Force B acts at 140° from the positive x-axis, and force C acts at 15° from the positive x-axis. The weight acts down with a magnitude of W = 100 kN. Use the equations of equilibrium to determine the magnitudes of B and C such that particle A is in equilibrium. For problems 2-5, consider the following scenario. Equilibrium of a particle: EF=0 XFx=0 and ΣFy=0. Dimensions are: h = 2.5 ft, d₁ = 4.75 ft, and d₂ = 3 ft. Give numeric answers to three significant figures. The load W = 50 lb. d₁ dz A h α W BSuppose a car approaches a hill and has an initial speed of 120 km/h at the bottom of the hill. The driver takes her foot off of the gas pedal and allows the car to coast up the hill. Note: the 790-kg car with an initial speed of 120 km/h is observed to coast up a hill and stops at a height 21 m above its starting point. a.) What is the magnitude of the average force of friction, in newtons, if the hill has a slope 2.7° above the horizontal?Two spheres A and B are placed in the arrangement shown below. If mA = 3m and mB = 8m, where on the dashed line should a third sphere C of mass 8m be placed so that the net force on it is zero? (b) If the distance between the two spheres A and B is 500 cm, find the location for the third sphere C so that the net force on it is zero. cm to the right of sphere B *answer for b*
- A block of mass m is being pulled by the string as shown below. The string has a tension T and makes an angle with the horizontal. If the block is initially at rest, find an expression for the velocity of the block after is has been moved a distance d. Your expression should only contain terms such as the tension, the coefficient of kinetic friction, the angle, d, etc. m T 0 HkA uniform density sheet of metal is cut into the shape of an isosceles triangle, which is oriented with the base at the bottom and a corner at the top. It has a base B = 43 cm, height H = 25 cm, and area mass density σ. - The horizontal center of mass of the sheet will be located: On the center line. Not enough information to determine. To the left of the center line. To the right of the center line. - The vertical center of mass of the sheet will be located: Below the mid height. Not enough information to determine. Above the mid height. At the mid height. - Write a symbolic equation for the total mass of the triangle. -Consider a horizontal slice of the triangle that is a distance y from the top of the triangle and has a thickness dy. Write an equation for the area of this slice in terms of the distance y, and the base B and height H of the triangle. - Set up an integral to calculate the vertical center of…A pulley is attached to one end of a rough plank, which makes an angle of 34◦ with the horizontal. A box is held at rest on the plank by a string that is attached to the box and passes over the pulley. A bucket of water is attached to the other end of the string and hangs freely. The coefficient of static friction between the plank and the box is 0.8. The box remains at rest but is on the point of slipping up the plank. The bucket of water has mass 7.5 kg.Name the four forces acting upon the box and draw a force diagram showing them, including the angles that show their directions.
- Please answer the correctly and clearlyAt the local hockey rink,a puck with a mass of 0.12 kg is given an initial speed of v = 5.3 m>s.(a) If the coefficient of kinetic friction between the ice and the puckis 0.11, what distance d does the puck slide before coming to rest?(b) If the mass of the puck is doubled, does the frictional force Fexerted on the puck increase, decrease, or stay the same? Explain.(c) Does the stopping distance of the puck increase, decrease, orstay the same when its mass is doubled? Explain. (d) For the situation considered in part (a), show that Fd = 12mv2. (In Chapter 7we will see 12mv2 is the kinetic energy of an object.)Calculate P required to move block A upward. Assume the coefficient of friction is 0.2 below block B. Neglect friction at all other contact surfaces. 30° P B 80 lb H₂ = 0.2 A 120 lb