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
(a) Well, it looks like the block is in quite a sticky situation, or should I say "slappy" situation? But let's not slap the physics in the face, and calculate the acceleration!
The gravitational force acting on the 10kg block can be calculated by multiplying the mass by the acceleration due to gravity (9.8 m/s²):
Gravity on the block = 10kg * 9.8 m/s² = 98 N
Now, let's determine the maximum static friction that the slap can provide. The coefficient of static friction is 9.60, so the maximum static friction force is:
Maximum static friction on the block = 9.60 * 40kg * 9.8 m/s² = 3763.20 N
Since the force being applied to the block is 100 N, which is less than the maximum static friction force, the block won't start moving yet. Therefore, the acceleration of the block is 0 m/s². It's just chillin' on top of the slap, enjoying the ride.
(b) As for the slap, there is no external force acting on it horizontally, other than the frictional force exerted by the block. The slap is simply supporting the block, so its acceleration will be the same as the block's. Therefore, the slap's acceleration is also 0 m/s².
So, to sum it up: the block and the slap aren't going anywhere anytime soon. They're both experiencing an acceleration of 0 m/s². It's like a static friction party on the slap!
To determine the acceleration of the block and the slab, we need to consider the forces acting on each object.
(a) Acceleration of the block:
Step 1: Calculate the gravitational force acting on the block:
F_gravity_block = m_block * g
F_gravity_block = 10 kg * 9.8 m/s^2
F_gravity_block = 98 N
Step 2: Calculate the maximum static frictional force acting on the block:
F_friction_block_max = μ_static * F_normal
F_friction_block_max = 0.40 * F_gravity_block (since the normal force is equal to the gravitational force for an object resting on a horizontal surface)
F_friction_block_max = 0.40 * 98 N
F_friction_block_max = 39.2 N
Step 3: Determine if the applied force (100 N) is less than the maximum static frictional force:
Since the applied force (100 N) is greater than the maximum static frictional force (39.2 N), the block will start moving and static frictional force is no longer applicable.
Step 4: Calculate the net force on the block:
F_net_block = F_applied - F_friction_block_max
F_net_block = 100 N - 39.2 N
F_net_block = 60.8 N
Step 5: Calculate the acceleration of the block using Newton's second law:
F_net_block = m_block * a_block
a_block = F_net_block / m_block
a_block = 60.8 N / 10 kg
a_block = 6.08 m/s^2
Therefore, the acceleration of the block is 6.08 m/s^2.
(b) Acceleration of the slab:
The slab is on a frictionless surface, so there is no frictional force acting on it. Thus, the only force acting on the slab is the gravitational force.
Step 1: Calculate the gravitational force acting on the slab:
F_gravity_slab = m_slab * g
F_gravity_slab = 40 kg * 9.8 m/s^2
F_gravity_slab = 392 N
Step 2: Determine the acceleration of the slab using Newton's second law:
F_net_slab = m_slab * a_slab
Since there are no other forces acting on the slab except for gravity:
F_net_slab = F_gravity_slab = m_slab * a_slab
392 N = 40 kg * a_slab
a_slab = 392 N / 40 kg
a_slab = 9.8 m/s^2
Therefore, the acceleration of the slab is 9.8 m/s^2.
To find the acceleration of the block and the slab, we first need to calculate the net force acting on each object.
(a) Acceleration of the block:
The block experiences two forces:
1. Force of gravity acting downwards: F_gravity = m_block * g, where m_block is the mass of the block (10 kg) and g is the acceleration due to gravity (9.8 m/s^2).
F_gravity = 10 kg * 9.8 m/s^2 = 98 N (downward)
2. Force applied to the block: F_applied = 100 N (given)
The net force acting on the block is the difference between the applied force and the force of gravity:
F_net = F_applied - F_gravity
= 100 N - 98 N
= 2 N (upward)
Now, we can calculate the acceleration of the block using Newton's second law:
F_net = m_block * a_block
2 N = 10 kg * a_block
a_block = 0.2 m/s^2
Therefore, the acceleration of the block is 0.2 m/s^2.
(b) Acceleration of the slab:
Since the slab is on a frictionless surface, there is no opposing force, and therefore, no acceleration. The slab will remain at rest.
Therefore, the acceleration of the slab is 0 m/s^2.
coef of friction = 9.60 ? That is very unusual.
Is a slap a slab ?
Is a flow something a floor?
There are two conditions here.
The first is before the block starts to slip on the slap and the static friction rules
In that case
F = 100 N
m = 40 + 10 = 50 kg
a = 100/50 = 2 m/s^2
Now will the block ever slip on the slab with a coef of 9.60?
F = 100 N
normal force = 9.81*10 = 98.1
maximum friction force = 98.1*9.60
so the block will never slip on the slab
HOWEVER I do not believe your 9.60
for reasonable friction if slipping:
F on block = 100 - mu*98.1
a block = (100 -mu*98.1)/10
a slab = mu*98.1 / 40