1. Two blocks on a frictionless horizontal surface are connected by a light string.
where m1 = 6.21 kg and m2 = 19.5 kg. A force of 48.4 N
6.21kg --T-- 19.5kg ----->48.4 N
The acceleration of gravity is 9.8 m/s^2. Find the acceleration of the system.
Answer in units of m/s^2.
2. What is the tension in the string between the blocks?
Answer in units of N.
3. If the surface were frictional, and the coefficient of kinetic friction between each block and the surface is 0.1, what would be the new
acceleration?
Answer in units of m/s^2.
4. What would be the new tension in the
string between the blocks?
Answer in units of N
To find the acceleration of the system, we can use Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, the net force is the tension in the string minus the force applied (48.4 N). Let's call the tension T.
1. To find the acceleration (a), we can set up the following equation:
T - 48.4 N = (m1 + m2) * a
Substituting the given values:
T - 48.4 N = (6.21 kg + 19.5 kg) * a
Solve for T:
T = (6.21 kg + 19.5 kg) * a + 48.4 N
The resulting tension value will be in units of Newtons (N).
2. To find the tension in the string between the blocks, you can substitute the known values into the equation we derived in step 1 and solve for T. The resulting value will be in units of Newtons (N).
3. If the surface has friction, we need to account for the frictional force in our equation. The frictional force can be calculated by multiplying the coefficient of kinetic friction (μk) with the normal force (N) acting on each block. The normal force is equal to the weight of each block (m * g), where g is the acceleration due to gravity (9.8 m/s^2).
The frictional force (Ffriction) is given by:
Ffriction = μk * N
For each block, N = m * g, so
Ffriction = μk * m * g
With friction present, the net force acting on each block is now the tension force (T) minus the frictional force (Ffriction). We will assume both blocks experience the same frictional force.
To find the new acceleration (a'), we need to adjust our equation from step 1:
T - Ffriction = (m1 + m2) * a'
Substituting the given values:
T - (μk * (m1 * g + m2 * g)) = (m1 + m2) * a'
Solve for a':
a' = (T - (μk * (m1 * g + m2 * g))) / (m1 + m2)
The resulting acceleration value will be in units of m/s^2.
4. To find the new tension in the string between the blocks, you can use the same equation as in step 3 and substitute the known values. The resulting tension value will be in units of Newtons (N).