A cart with a mass of 20kg is initially at rest on a horizontal frictionless sur

Question

A cart with a mass of 20kg is initially at rest on a horizontal frictionless surface and is attached to a block of 5kg hanging vertically.

I.) When the blocks are released and accelerating, what is the tension in the rope?

a. T = 25 N

b. T = 39 N

c. T = 49 N

II.) If the block was initially hanging 2m above the ground, what is the final velocity of the block right before it hits the ground?

a. v = 1.6 m/s

b. v = 2.1 m/s

c. v = 2.8 m/s

III.) What coefficient of friction between cart and surface would be needed to keep the system from accelerating? (Using 20 kg as the mass of the cart.)

a. 0.20

b. 0.25

c. 0.50

IV.) In this situation (with friction), how does the tension in the rope compare with the weight of the hanging block?

a. they are equal

b. the tension is greater than the weight of the block

c. the tension is less than the weight of the block.

Explanation / Answer

here,

mass of cart, mc = 20 kg

mass of block, mb = 5 kg

Part A:
From newton second law : SUM(F) = 0
For box:
T - mb*g = - mb*a ( t is tension in string)
acceleration, a = - (T - mb*g)/mb ------(1)

For cart:
Tension in string, T = mc * a
Tension in string, T = 20 * -(T - mb*g)/mb ( From eqn 1)
Tension in string, T = 20 * -(T - 5*9.81)/5
Tension in string, T = 39.4 N or 39 N

Option B is correct

Part B:
acceleration of block, a = - (T - mb*g)/mb
acceleration of block, a = - (39 - 5*9.81)/5
acceleration of block, a = 2.01 m/s^2

height of block, h = 2 m

From third eqn of motion:
v^2 = 2*a*h
velocity = sqrt(2*2.01*2)
velocity = 2.8 m/s^2

option C is correct

Part C:
From newton second law : SUM(F) = 0
T - Ff = mc * a ( Ff is frictional force)
T - u*mc*b = mc * 0
39 - u * 20 * 9.81 = -20 * 0
coefficient of friction, u = 0.2

Option A is correct

Part D:
Weight of block, w = mb * g
Weight of block, w = 5 * 9.81
Weight of block, w = 49.05 N

Since W > T

so the block will move downwards

Option C is correct

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.