A 5.0 kg block is placed on top of a 10. kg block (ux1.eiu.edu/~cfadd/1350/Hmwk/Ch05/Images/P5.74.gif) . A horizontal force of 45 N is applied to the 10. kg block and the 5.0 kg block is tied to the wall. The coefficient of friction between the moving surfaces is 0.20.
1. Determine the tension in the string that ties the 5.0 kg block to the wall
2. Determine the acceleration of the 10. kg block.
To solve this problem, we need to consider the forces acting on the system. Let's break it down step by step:
Step 1: Identify the forces acting on the 10 kg block.
a) Weight (also known as Gravitational Force): The weight of the 10 kg block can be found using the formula:
Weight = mass * acceleration due to gravity (g)
Weight = 10 kg * 9.8 m/s² = 98 N (downward)
b) Normal force: The normal force is the force exerted by a surface to support the weight of the object resting on it. Since the 10 kg block is on a horizontal surface, the normal force is equal to its weight, which is 98 N (upward).
c) Applied force: The force applied to the block is 45 N (to the right).
d) Friction force: The friction force is given by the formula:
Friction force = coefficient of friction * normal force
Friction force = 0.20 * 98 N = 19.6 N (opposite to the direction of motion, to the left)
Step 2: Calculate the net force acting on the 10 kg block.
Net force = Applied force - Friction force
Net force = 45 N - 19.6 N = 25.4 N (to the right)
Step 3: Apply Newton's second law of motion.
Net force = mass * acceleration
25.4 N = 10 kg * acceleration
acceleration = 2.54 m/s² (to the right)
Step 4: Determine the tension in the string.
The 5 kg block is tied to the wall, so the tension in the string is equal to the weight of the 5 kg block (downward):
Tension in the string = weight of the 5 kg block
Tension in the string = 5 kg * 9.8 m/s² = 49 N (downward)
Therefore, the tension in the string that ties the 5.0 kg block to the wall is 49 N.
To summarize:
1. The tension in the string is 49 N (downward).
2. The acceleration of the 10 kg block is 2.54 m/s² (to the right).
To solve these problems, let's break it down step by step:
First, let's address the tension in the string (the force pulling the 5.0 kg block towards the wall).
1. To find the tension, we need to consider the forces acting on the 5.0 kg block. There are three forces involved: the weight of the block (mg), the normal force (N), and the force of static friction (fs). The tension in the string (T) is equal to the force of static friction.
The weight of the block can be calculated by multiplying the mass (m) by the acceleration due to gravity (g). In this case, the weight of the 5.0 kg block would be (5.0 kg) x (9.8 m/s^2) = 49 N.
The normal force (N) is equal to the weight of the 10. kg block, which is 10. kg x 9.8 m/s^2 = 98 N. This is because the 5.0 kg block presses down on the 10. kg block with a force equal to its weight.
The force of static friction (fs) can be calculated by multiplying the coefficient of friction (μ) by the normal force (N). In this case, fs = (0.20) x (98 N) = 19.6 N.
Therefore, the tension in the string is equal to the force of static friction, which is 19.6 N.
Now, let's address the acceleration of the 10. kg block.
2. To find the acceleration, we need to consider the forces acting on the 10. kg block. There are three forces involved: the applied horizontal force (F), the force of static friction (fs), and the weight of the block (mg).
The weight of the block can be calculated using the same formula as before: (10. kg) x (9.8 m/s^2) = 98 N.
The force of static friction (fs) can also be calculated using the same formula as before: fs = (0.20) x (98 N) = 19.6 N.
To find the acceleration, we use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration (Fnet = ma). In this case, the net force is the applied horizontal force minus the force of static friction (F - fs).
Substituting the known values, we get: F - fs = ma
Rearranging the equation, we can solve for acceleration: a = (F - fs) / m
Plugging in the values, we get: a = (45 N - 19.6 N) / 10. kg
Solving the equation, we find that the acceleration of the 10. kg block is 2.26 m/s^2.