A 25.1 kg mass is sliding to the right along a horizontal surface, beign pulled by a force of 152 N that directed up-and-to-the-right at 31.3 degrees above horzontal. The coefficient of kineticfriction is 0.329. Find the acceleration of the mass.

Sure, let's solve this step by step:

Step 1: Identify the forces acting on the mass. There are three forces acting on the mass:

• The gravitational force (Fg = m*g), acting downwards
• The pulling force (Fp), acting up-and-to-the-right at an angle of 31.3 degrees
• The frictional force (Ff = μ*N), acting to the left

Step 2: Resolve the forces into their components. The pulling force can be resolved into two components: Fpx (horizontal) and Fpy (vertical).

• Fpx = Fpcos(31.3) = 152cos(31.3) = 130.2 N
• Fpy = Fpsin(31.3) = 152sin(31.3) = 78.8 N

Step 3: Calculate the normal force. The normal force (N) is the force exerted by a surface that supports the weight of an object resting on it. It acts perpendicular to the surface. The normal force here is the weight of the object minus the vertical component of the pulling force.

• N = Fg - Fpy = mg - Fpy = 25.19.8 - 78.8 = 167.2 N

Step 4: Calculate the frictional force. The frictional force (Ff) is the force exerted by a surface as an object moves across it or makes an effort to move across it.

• Ff = μN = 0.329167.2 = 55.0 N

Step 5: Calculate the net force. The net force (Fnet) is the vector sum of all the forces. In this case, it's the horizontal component of the pulling force minus the frictional force.

• Fnet = Fpx - Ff = 130.2 - 55.0 = 75.2 N

Step 6: Calculate the acceleration. Finally, we can find the acceleration (a) using Newton's second law (F = m*a).

• a = Fnet/m = 75.2/25.1 = 3.0 m/s²

So, the acceleration of the mass is 3.0 m/s².