A block of mass 1 kg lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is 0.6, If the acceleration of the truck is 5 m/s2, the frictional force acting on the block is :A 5 N B 6 N C 10 N D 15 N
Question
A block of mass 1 kg lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is 0.6, If the acceleration of the truck is 5 m/s2, the frictional force acting on the block is :A 5 N B 6 N C 10 N D 15 N
Solution
To solve this problem, we first need to calculate the maximum static friction force. The formula for this is:
f_max = μN
where:
- f_max is the maximum static friction force
- μ is the coefficient of static friction
- N is the normal force
In this case, the block is not moving vertically, so the normal force is equal to the weight of the block. The weight can be calculated as:
W = mg
where:
- W is the weight
- m is the mass
- g is the acceleration due to gravity, which is approximately 9.8 m/s²
So, N = W = 1 kg * 9.8 m/s² = 9.8 N
Now we can calculate the maximum static friction force:
f_max = μN = 0.6 * 9.8 N = 5.88 N
This is the maximum force of static friction, which means it's the maximum force that can be applied to the block without it moving. If the truck is accelerating at 5 m/s², the force required to keep the block from moving (i.e., the force of static friction) is:
F = ma
where:
- F is the force
- m is the mass
- a is the acceleration
So, F = 1 kg * 5 m/s² = 5 N
Since 5 N is less than the maximum static friction force of 5.88 N, the block will not move, and the frictional force acting on the block is 5 N. So, the answer is A: 5 N.
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