#1.) If the force of gravity on a human is 539 N determine the mass of the human.
#2.) Draw a free body diagram for the following situation:
a.) A 0.15 kg running shoe is pushed to the right, with a constant velocity, across a wet concrete floor with an applied force of 3.5 N.
b.) Calculate the normal force exerted by the concrete onto the running shoe.
#3.) Draw a free body diagram of a boat being pulled at an accelerated rated by a truck down a highway.
#1.) Oh, the gravity of the situation! To find the mass of the human, we can use Newton's second law: F = ma. Given that the force of gravity is 539 N, we can divide that by the acceleration due to gravity (approximately 9.8 m/s^2) to find the mass. So, let's do the math: 539 N / 9.8 m/s^2 = approximately 55 kg. There you have it - the human has a weighty mass of 55 kg!
#2.) a.) Well, it seems we have a shoe-tuation here! Let's draw a free body diagram for this situation. We have a 0.15 kg running shoe being pushed to the right with a constant velocity and an applied force of 3.5 N. So, on our diagram, we can show an arrow pointing to the right to represent the applied force of 3.5 N, and label it as the applied force. Since the shoe is at a constant velocity, we can also draw a balanced force arrow pointing to the left, representing the force of friction. That should do the trick!
b.) Now, let's talk about the normal force. Ah, the shoe is making contact with the wet concrete floor. The normal force is what keeps us from falling through the floor, so it must counteract the weight of the shoe. In this case, the normal force equals the weight of the shoe. Since the shoe has a mass of 0.15 kg and we know the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight using the formula weight = mass * acceleration due to gravity. So, the weight of the shoe is 0.15 kg * 9.8 m/s^2 = 1.47 N. Therefore, the normal force exerted by the concrete onto the running shoe equals 1.47 N. It's like the concrete is giving the shoe a little boost... or, you know, normal force!
#3.) Ah, the boat and truck tango on the highway! Let's draw a free body diagram for this accelerated adventure. We'll have the boat as our main focus, being pulled by the truck. So, we'll start by drawing an arrow pointing to the right to represent the force of the truck pulling the boat, labeling it as the pulling force. Since the boat is being accelerated, we'll also add another arrow pointing to the right to represent the boat's acceleration, labeling it as the boat's acceleration. Lastly, we can show an arrow pointing to the left to represent the frictional force between the boat and the road, labeling it as the frictional force. Just imagine that boat cruising on the highway, being the star of the free body diagram show!
#1.) To determine the mass of the human, we can use the equation F = mg, where F is the force of gravity and g is the acceleration due to gravity (approximately 9.8 m/s^2). Rearranging the equation, we get m = F/g.
To find the mass, divide the force of gravity by the acceleration due to gravity:
m = 539 N / 9.8 m/s^2
Calculating the answer, we get:
m ≈ 55 kg
Therefore, the mass of the human is approximately 55 kg.
#2.) a.) To draw a free body diagram for the running shoe on the wet concrete floor, we need to identify the forces acting on it.
The forces involved are:
- Applied force pushing the shoe to the right (3.5 N)
- Force of gravity acting downwards (weight of the shoe)
- Normal force exerted by the floor (perpendicular to the surface)
- The frictional force opposing the motion (if any)
b.) To calculate the normal force exerted by the concrete onto the running shoe, we need to consider that the shoe is in equilibrium since it is moving at a constant velocity.
In this case, the normal force is equal in magnitude and opposite in direction to the force of gravity acting on the shoe. Therefore, the normal force is equal to the weight of the shoe.
So, the normal force exerted by the concrete onto the running shoe is equal to the weight of the shoe, which can be calculated using the formula:
Weight = mass × acceleration due to gravity
Given that the mass of the shoe is 0.15 kg, and the acceleration due to gravity is 9.8 m/s^2, we can calculate the normal force:
Normal force = 0.15 kg × 9.8 m/s^2
Calculating the answer, we get:
Normal force ≈ 1.47 N
Therefore, the normal force exerted by the concrete onto the running shoe is approximately 1.47 N.
#3.) To draw a free body diagram of a boat being pulled at an accelerated rate by a truck down a highway, we need to identify the forces acting on the boat.
The forces involved are:
- Applied force by the truck, directed forward
- Force of friction opposing the direction of motion
- Force of gravity acting downwards (weight of the boat)
- Buoyant force (if the boat is in the water)
- Normal force (if the boat is on a surface)
These forces can vary depending on the specific situation and environment, but the diagram should capture the forces mentioned above.