To practice Problem-Solving Strategy 6.1 Work and Kinetic Energy. Your cat “Ms.”

Question

To practice Problem-Solving Strategy 6.1 Work and Kinetic Energy.

Your cat “Ms.” (mass 8.50 kg ) is trying to make it to the top of a frictionless ramp 2.00 m long and inclined 19.0 above the horizontal. Since the poor cat can’t get any traction on the ramp, you push her up the entire length of the ramp by exerting a constant 52.0 N force parallel to the ramp. If Ms. is moving at 1.70 m/s at the bottom of the ramp, what is her speed when she reaches the top of the incline?

PART A

The initial and final positions of the cat are at the bottom and the top of the ramp, respectively. Since the forces acting on the cat are constant, a free-body diagram can be drawn at any arbitrary position in her motion.

Use the diagram below to draw a free-body diagram showing all the forces acting on the cat. The cat is represented by the black dot.

Draw the vectors starting at the black dot. The location and orientation of the vectors will be graded. The length of the vectors will not be graded.

Part B

What is the cat's speed v2 when she reaches the top of the incline?

Express your answer in meters per second to three significant figures.

Explanation / Answer

theta = 19 degree

mass , m = 8.5 Kg

F = 52 N

v = 1.70 m/s

a)

b)

Now, for the acceleration of mass is a

m * a = F - m *g * sin(theta)

8.5 * a = 52 - 8.5 * 9.8 * sin(19)

solving for a

a = 2.93 m/s^2

Now , for the speed v2

v2^2 - 1.70^2 = 2 * 2.93 * 2

solving for v2

v2 = 3.82 m/s

the cat's speed v2 when she reaches the top of the incline is 3.82 m/s

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