Question

what net torque must be applied

1. A ball is rolled horizontally off a table with an initial speed of 0.24 m/s. A stop watch measures the ball's trajectory time from table to the floor to be 0.30 s. How far away from the table does the ball land? (g=9.8 m/s2 and air resistance is negligible) a. 0.055 m b. 0.072 m c. 1.2 m d. 1.9 m 2. A disk has a moment of inertia of 3.0 x 10-4 kg.m2 and rotates with an angular speed of 3.5 rad/sec. What net torque must be applied to bring it to rest within 3 s? a. 4.5 x 10-3 Nm b. 7.5 x 10-4 N.m c. 5.0 x 10-4 N·m d. 3.5 x 10-4 N·m

Answer 1

1Sol:

initial speed,u= 0.24 m/s but speed is horizontal so it doesn't have any vertical component.

but the trajectory moving took t=0.30 s so it has been in the air for 0.30s with a 0.24 m/s horizontal speed.

then

Distance, S =ut+0.5at^2 where acceleration a=0 for horizontal then S would be

S = 0.24 * 0.30 = 0.072 m

so it lands 0.072 m far from the table.

2.sol:

W = Angular speed,

W₀ = initial angular frequency,

a = angular acceleration,

t = time,

I = Moment of Inertia

W = W₀ + a*t

Torque,? = I*a,

therefore a = ? / I

considering initial angular speed is zero we get

W = [t*?/ I] ,

? = W*I / t

Torque = 3.5*3.0 x 10^-4 / 3

Net Torque = 3.5x10^^-4 Nm