10kg block rest on top of a 40kg slap which rest on a frictionless flow. the coefficient of static and friction between the block and the slap are 9.60 and 0.40 respectively. the block is pulled with a force of 100 Newton. what are the acceleration of (a) the block (b) the slap
To find the acceleration of both the block and the slab, you need to consider the forces acting on each object.
(a) Acceleration of the block:
1. First, calculate the force of static friction acting on the block. The formula is:
F_friction = coefficient of static friction * normal force
The normal force acting on the block is equal to its weight, which is mass * gravity:
normal force = 10 kg * 9.8 m/s^2 = 98 N
F_friction = 0.40 * 98 N = 39.2 N
2. Since the block is pulled with a force of 100 N, the net force acting on the block is the difference between the applied force and the force of friction:
net force = applied force - force of friction
net force = 100 N - 39.2 N = 60.8 N
3. Finally, use Newton's second law of motion to find the acceleration of the block:
F_net = mass * acceleration
60.8 N = 10 kg * acceleration
acceleration = 60.8 N / 10 kg = 6.08 m/s^2
Therefore, the acceleration of the block is 6.08 m/s^2.
(b) Acceleration of the slab:
Since the slab is resting on a frictionless floor, there is no force of friction acting on it. Therefore, the only horizontal force acting on the slab is the force exerted by the block.
The force exerted by the block on the slab is equal to the force of friction acting on the block, which we already calculated in step 1 as 39.2 N.
Use Newton's second law to find the acceleration of the slab:
F_net = mass * acceleration
39.2 N = 40 kg * acceleration
acceleration = 39.2 N / 40 kg = 0.98 m/s^2
Therefore, the acceleration of the slab is 0.98 m/s^2.