1. A car with 60 cm diameter tires is traveling at a constant speed of 100 km/hr

Question

1. A car with 60 cm diameter tires is traveling at a constant speed of 100 km/hr. What is the angular velocity of the tires in rad/s?
2. A 3kg ball is traveling in a circle of radius 2 meters with a tangential velocity of 2 meters/second. find the centripetal acceleration of the ball and the centripetal force acting on it.
3. An arrow is shot at an angl such that it's horizontal velocity is 40 m/s an it's vertical velocity is 20 m/s. Find the horizontal distance the arrow will travel before hitting the ground.
4. A bolt requires 15 Nm or torque to loosen it. How much force needs to be applied to a 20 cm long wrench to loosen the bolt? Assume the force is applied perpendicular to the handle of the wrench.
5.A baseball is thrown such that it is in the air for 4 seconds and lands 100 m away. Find the initial vertical and horizontal components of the baseball's velocity.

Explanation / Answer

a) r = 30cm= 0.3m , v = 100km/hr= 27.78 m/s apprx

( angular velocity)= v/r = 27.78/0.3=92.59 rad/sec apprx

b) ac( centripetal acceleration) = v^2/r = 2^2/2= 2 m/s^2

F orce= ma= 3(2) = 6N

c) angle at which the arrow is shot = tan= 20/40= 0.5

= tan^-1(0.5)=26.56 degree apprx

horizontal distance = range= 2usinucos/g = 2( 20)(40)/9.8=163.265 m apprx

d) = F x r

F = /r = 15/0.2=75 N

e)Tf= total flight time = 4seconds= 2(usin)/g

usin(vertical componnet of velocity) = 4x9.8/2= 19.6 m/s apprx

range= 100 = 2usinucos/g

100x9.8= 2( 19.6) ucos

ucos= 25m/s ( horizontal componet)

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