Max Accel & Force for Mass Block & Cart

[PhysicslyDSBL]

Homework Statement

A block of mass mblock = 1.5 kg rests on a cart of mass mcart = 3.5 kg, which moves without friction on a horizontal surface. The coefficient of static friction between the block and the cart is µ = 0.7. The cart is accelerating to the right.

a) What is the maximum acceleration such that the block does not slide on the cart?


b) What is the magnitude of the force on the cart required to provide the acceleration amax?

Homework Equations

a) and b) F=ma

The Attempt at a Solution

a) I got a by taking the mass of the block and multiplying it by gravity ---> 1.5*9.8=14.7N
Then I took 14.7N and multiplied that by mew ---> 14.7*0.7 = 10.29
I then took this number, and divided it by the mass of the block --->
10.29/1.5 = 6.86 m/s^2

So 6.86m/s^2 is the max acceleration so wouldn't this make 10.29 the magnitude of the force required to provide the acceleration for amax?

 

[alphysicist]

Hi PhysicslyDSBL,

Homework Statement

A block of mass mblock = 1.5 kg rests on a cart of mass mcart = 3.5 kg, which moves without friction on a horizontal surface. The coefficient of static friction between the block and the cart is µ = 0.7. The cart is accelerating to the right.

a) What is the maximum acceleration such that the block does not slide on the cart?


b) What is the magnitude of the force on the cart required to provide the acceleration amax?

Homework Equations

a) and b) F=ma

The Attempt at a Solution

a) I got a by taking the mass of the block and multiplying it by gravity ---> 1.5*9.8=14.7N
Then I took 14.7N and multiplied that by mew ---> 14.7*0.7 = 10.29
I then took this number, and divided it by the mass of the block --->
10.29/1.5 = 6.86 m/s^2

So 6.86m/s^2 is the max acceleration so wouldn't this make 10.29 the magnitude of the force required to provide the acceleration for amax?

That is the required force on the cup to give it an acceleration of a_max. But they want the required force on the cart to give the entire system an acceleration of a_max.

 

[baba89]

Your approach and calculations seem to be correct. The maximum acceleration that the cart can have without the block sliding is 6.86 m/s^2. This means that the magnitude of the force required to provide this acceleration is 10.29 N. It is important to note that this force is the maximum force that can be applied without causing the block to slide. Any force greater than this value would cause the block to slide.