Answer to Question #292389 in Mechanics | Relativity for bookaddict

Question

A mass of 20 kg is being pulled, with a rope, up a frictionless slope inclined at an angle of 30°. The rope is parallel to the slope, and the mass is traveling at a constant 5 ms-1 in a straight line.

a. Draw a free-body diagram for this situation.

b. Draw a vector triangle for the weight, dividing it into perpendicular components.

c. Calculate the component of the weight that is parallel to the slope.

d. Hence calculate the work done in pulling the mass 3 metres.

e. What is the power required?

f. How much gravitational potential energy has the mass gained when pulled 3 metres along the slope?

g. The 20 kg mass is then released from rest on another 30° slope, but this time there is a frictional force of 15 N. Find the magnitude and direction of the acceleration in this case.

Answer 1

a, b. Please see the drawing below:

c. Calculate the component of the weight that is parallel to the slope:

$$W_x=mg\sin\theta=98\text{ N}.$$

d. Hence calculate the work done in pulling the mass 3 metres:

$$W=W_xd=294\text{ J}.$$

e. What is the power required?

$$P=W_xv=490\text{ W}.$$

f. How much gravitational potential energy has the mass gained when pulled 3 metres along the slope?

$$E_p=mgh=mgd\sin\theta=294\text{ J}.$$

g. The 20 kg mass is then released from rest on another 30° slope, but this time there is a frictional force of 15 N. The magnitude of acceleration can be found by Newton's third law:

$$ma=W_x-f→a=\dfrac{W_x-f}{m}=4.15\text{ m/s}^2.$$

The direction of the acceleration in this case is toward the bottom of the slope.