Can someone help me with this problem? It requires a lot of visualizing and I've never been great at problems like that.
A pair of blocks of mass m1 =29.0 kg, and m2 =58.0 kg, are being pushed on a horizontal surface by a constant forces of magnitude F=87.0 N. The angle θ = 31.4 ° . The blocks are displaced 7.5 m, assume there is no friction between the bottom of the blocks and the floor. Block m1 is to the left of block m2 and both are lying flat on the surface.
a) How many forces are acting on the system made up of both blocks (treat both blocks as one)?
b) What is in Newtons the magnitude of the net force acting on the system made up of both blocks?
c) What is in Newtons the magnitude of the net force acting on m1?
d) What is in Newtons the magnitude of the force exerted by m1 on m2?
e) What is in Newtons the magnitude of the force exerted by m2 on m1?
Use 10.0 N/kg for g.
To solve this problem, we need to break it down into smaller steps. Let's go through each part of the problem one by one.
a) To determine the number of forces acting on the system made up of both blocks, we need to consider the external forces. In this case, the external force is the constant force F of magnitude 87.0 N. Therefore, there is only one force acting on the system.
b) The net force acting on the system made up of both blocks can be calculated by summing up the vectors of all the external forces. In this case, since there is only one external force (F), the magnitude of the net force is equal to the magnitude of the external force, which is 87.0 N.
c) To calculate the net force acting on m1, we need to consider the individual forces acting on m1. There are two forces acting on m1: the force due to the external force F, and the force exerted by m2 on m1. The force due to the external force F is directed to the right, and the force exerted by m2 on m1 is directed to the left. Since the forces have opposite directions, we need to subtract the magnitude of the force exerted by m2 on m1 from the magnitude of the external force F to find the net force acting on m1.
d) The magnitude of the force exerted by m1 on m2 is equal in magnitude but opposite in direction to the force exerted by m2 on m1. Therefore, the magnitude of the force exerted by m1 on m2 is the same as the magnitude of the force exerted by m2 on m1.
e) As mentioned in part d, the magnitude of the force exerted by m2 on m1 is the same as the magnitude of the force exerted by m1 on m2.
Now, let's calculate the answers to parts c), d), and e) using the given information.
Given:
m1 = 29.0 kg,
m2 = 58.0 kg,
F = 87.0 N,
θ = 31.4°,
g = 10.0 N/kg,
displacement = 7.5 m.
To solve these parts, we'll need to use Newton's laws of motion and some trigonometry. Let's calculate the forces using the following formulas:
Net force on m1 = F * cos(θ) - force exerted by m2 on m1
Magnitude of the force exerted by m1 on m2 = Magnitude of the force exerted by m2 on m1 = F * sin(θ)
Substituting the given values into the formulas:
c) Net force on m1 = 87.0 N * cos(31.4°) - force exerted by m2 on m1
d) Magnitude of the force exerted by m1 on m2 = Magnitude of the force exerted by m2 on m1 = 87.0 N * sin(31.4°)
Now, you can calculate the values for parts c), d), and e) using a calculator.