Normal force, acceleration and tension

[livblue23]

Homework Statement

How do you find the normal force and acceleration of a 72 N block that is pulled across the floor with tension force of 33 degrees. As is slides the coefficient of kinetic friction between object and the floor is 0.32.

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

Homework Statement

How do you find the normal force and acceleration of a 72 N block that is pulled across the floor with tension force of 33 degrees. As is slides the coefficient of kinetic friction between object and the floor is 0.32.

Welcome to PF.

Generally the normal force is going to be m*g.

The Tension is apparently upwards which means that the upward component the tension T*Sinθ is pulling up and reducing the m*g

Whatever your normal force times the coefficient of friction is it will retard the forward pull of the Tension, which is the horizontal component of T.

 

[thomate1]

To find the normal force, we can use the equation F_N = mg, where F_N is the normal force, m is the mass of the block, and g is the acceleration due to gravity (9.8 m/s^2). Assuming the block is on a flat surface, the normal force would be equal to the weight of the block, which is 72 N in this case.

To find the acceleration, we can use Newton's second law, F = ma, where F is the net force acting on the block and a is the acceleration. In this case, the net force would be the tension force in the direction of motion minus the force of kinetic friction in the opposite direction. So we can write the equation as:

ma = T - μmg

Where T is the tension force (in this case, 33 N) and μ is the coefficient of kinetic friction (0.32). Solving for a, we get:

a = (T - μmg)/m

Substituting the values, we get:

a = (33 N - (0.32)(72 N))/m

Since we don't know the mass of the block, we can't determine the exact acceleration. However, we can say that the acceleration would be in the direction of the tension force, since that is the net force acting on the block.

In summary, to find the normal force and acceleration of the block, we need to know the mass of the block and the tension force, and we can use the equations F_N = mg and F = ma, respectively. The coefficient of kinetic friction can also be used to determine the net force acting on the block.