Final answer:
The tension in the string attached to the block is calculated by adding the force needed to overcome friction and the force required for the block's acceleration. The normal force is equal to the weight of the block, and the force of friction is the product of the coefficient of kinetic friction and the normal force. The total tension is found to be approximately 20 N.
Step-by-step explanation:
To find the tension in the string attached to a block on a horizontal surface, we must consider the force of friction and the net force required for the block's acceleration.
Given a block of mass 4.0 kg, a coefficient of kinetic friction of 0.20, and an acceleration of 3.0 m/s2, we first calculate the force of friction.
The force of friction (f) is given by f = μk * N, where μk is the coefficient of kinetic friction and N is the normal force. Since there is no vertical acceleration, the normal force (N) is equal to the weight of the block (W), which is W = mass (m) * gravity (g).
Thus, N = 4.0 kg * 9.80 m/s2
= 39.2 N
f = 0.20 * 39.2 N
= 7.84 N
Next, we apply Newton’s second law (F = m * a) to find the total horizontal force required for acceleration, which is
F = 4.0 kg * 3.0 m/s2
= 12.0 N
The tension in the string must overcome both the force of friction and provide the net force for acceleration, so the tension (T) is T = F + f
= 12.0 N + 7.84 N
= 19.84 N, which we can round to 20 N.