A small cube of mass m slides down a circular ramp of radius R cut into a large block of mass M, as shown. The large block rests on a table, and both blocks move without friction. The blocks are initially at rest, and the cube starts from the top of the path. Find the speed v of the cube the instant after it has 2gR left the block. [Ans: v² =- 1+ (m/M)
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![5. A small cube of mass m slides down a circular ramp of radius R cut into a large block of mass M, as
shown. The large block rests on a table, and both blocks move without friction. The blocks are initially
at rest, and the cube starts from the top of the path. Find the speed v of the cube the instant after it has
left the block. [Ans: v =2gR
1 + (m/M)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd767e2f1-cca9-465a-901b-5ef8f3218e51%2F0c1c7909-cb47-49e4-9418-cc4a1f871c6a%2Fecx1hef_processed.png&w=3840&q=75)
![M
Problem 5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd767e2f1-cca9-465a-901b-5ef8f3218e51%2F0c1c7909-cb47-49e4-9418-cc4a1f871c6a%2Fl442ib_processed.png&w=3840&q=75)
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- #4A object of mass 3.00 kg is subject to a force Fx that varies with position as in the figure below. A coordinate plane has a horizontal axis labeled x (m) and a vertical axis labeled Fx (N). There are three line segments. The first segment runs from the origin to (6,3). The second segment runs from (6,3) to (10,3). The third segment runs from (10,3) to (16,0). (a) Find the work done by the force on the object as it moves from x = 0 to x = 6.00 m. Your response differs from the correct answer by more than 10%. Double check your calculations. J(b) Find the work done by the force on the object as it moves from x = 6.00 m to x = 10.0 m. J(c) Find the work done by the force on the object as it moves from x = 10.0 m to x = 16.0 m. J(d) If the object has a speed of 0.600 m/s at x = 0, find its speed at x = 6.00 m and its speed at x = 16.0 m. speed at x = 6.00 m m/s speed at x = 16.0 m m/sA 0.1 kg ball is launched from a vertical cannon, 0.7 m high and 0.05 m wide. The cannon exerts a 146 N force on the ball for a period of 0.03 s. What is the final height ofthe ball?
- Two blocks are connected by a light string that passes over a frictionless pulley as in Figure 1. The system isreleased from rest while m2 is on the floor and m1 is a distance h above the floor.a) Assuming m1 > m2, find an expression for the speed of m1 just as it reaches the floor.b) Taking m1=6.5 kg, m2=4.2 kg, and h=3.2 m, evaluate your answer to part (a).c) Find the speed of each block when m1 has fallen a distance of 1.6m.Chapter 06, Problem 066 GO In the figure here, block 1 of mass 2.4 kg and block 2 of mass 3.4 kg are connected by a string of negligible mass and are initially held in place. Block 2 is on a frictionless surface tilted at 0 = 28 °. The coefficient of kinetic friction between block 1 and the horizontal surface is 0.28. The pulley has negligible mass and friction. Once they are released, the blocks move. What then is the tension in the string? Number Unit the tolerance is +/-5% Click if you would like to Show Work for this question: Open Show WorkA mass of m = 0.500 kg slides across a horizontal frictionless counter with a speed vo= 0.300 m/s. It then runs into and compresses a spring of spring constant k-750 N/m. ୪୪୪୩ d O Weight, Normal, Spring Force, Friction O Weight, Spring Force, Friction O Weight, Normal, Spring Force O Weight, Normal, Friction Physics Principles (a) Pick all forces act on the spring-mass system as the mass compresses the spring. (b) Which of these forces do not do any work? C C -VO Weight, Normal Force, Spring Force Weight, Normal Force Normal, Spring Force Weight, Friction m
- The figure below shows four objects at the corners of a rectangle, connected by rods of negligible mass. The center of the rectangle lies at the origin of an xy-coordinate system. The width of the rectangle (along the x-axis) is 4.00 m, and the height (along the y-axis) is 6.00 m. Starting at the top left and going clockwise, the masses of the objects are m, = 3.50 kg, m2 = 2.50 kg, m3 = 4.30 kg, and m, = 1.90 kg. m, m2 6.00 m m3 + 4.00 m→ (a) What is the moment of inertia (in kg • m2) of the system about the x-axis? kg • m2 (b) What is the moment of inertia (in kg · m2) of the system about the y-axis? kg • m (c) What is the moment of inertia (in kg · m2) of the system about an axis through O and perpendicular to the page (that is, the z-axis)? kg · m2A 1360 - kg car moving at 6.40 m/s is initially traveling north along the positive direction of a y axis. After completing a 90° right-hand turn to the positive x direction in 4.00 s, the inattentive operator drives into a tree, which stops the car in 490 ms. (picture has the question)A ball with mass m is attached to the end of a flagpole. The flagpole is connected to the side of a building at point P, has a length ℓ, and makes an angle θ with the x-axis. (Consider the +x-direction to be to the right, the +y-direction upward, and the +z-direction to be out of the page.) At time t = 0, the ball becomes loose and begins to fall off of the flagpole with acceleration −gĵ. (a) What is the angular momentum of the ball about point P as a function of time? (Use the following as necessary: m, ℓ, g, t, and θ. Express your answer in vector form.) (b) For what physical reason does the angular momentum change? (c) What is the rate of change of the angular momentum of the ball about point P? (Use the following as necessary: m, ℓ, g, and θ. Express your answer in vector form.)
- A block of mass m = 3.5 kg, initially moving at a speed of v_{1} = 12m / s to the right on a horizontal frictionless surface, is acted on by a variable horizontal force F as follows: For the first 10 s, F = 10N to the right; for the next 5 <= F =25* to the left; and for the last 8 <= F = 15N to right. Find the velocity of the block at the end of the 23-s interval.A block of mass m is initially at rest at the top of an inclined plane which has a height of 6.18m and makes an angle of θ=25.2∘ with respect to the horizontal. After being released, it is observed to be traveling at v=0.14m/s a distance d after the end of the inclined plane, as shown. The coefficient of kinetic friction between the block and the plane is μp=0.1, and the coefficient of friction on the horizontal surface is μr=0.2. Find the distance, d, in meters.A horizontal force of 80.0 N is applied to a 5.00 kg block as the block slides a distance of 0.800 m along a horizontal floor. The coefficient of kinetic friction between the floor and the block is 0.500. If the block is initially at rest, how fast is it moving at the end of the displacement?