A 6.110 kg block of wood rests on a steel desk. The coefficient of static friction between the block and the desk is μs = 0.455 and the coefficient of kinetic friction is μk = 0.255. At time t = 0, a force F = 16.8 N is applied horizontally to the block. State the force of friction applied to the block by the table at the following times:
Well, well, well. Looks like we've got a classic physics problem here. Let's find out what's cooking!
At time t = 0, when that force F = 16.8 N starts tickling the block, we need to figure out the force of friction applied by the table. Buckle up!
First, we need to check if the block is sitting still or if it's in motion. If it's not moving, we're dealing with static friction. Once it starts moving, we enter the realm of kinetic friction. Ready?
Let's start with the force of static friction, shall we?
Since the block is not moving initially, the applied force F is balanced by the force of static friction. So, the force of friction at t = 0 is equal to the applied force F, which is 16.8 N. Ta-dah!
Now, if that block starts moving, the force of static friction loses its charm and kinetic friction takes over.
To find that force of kinetic friction, we'll need the equation Fk = μk * N, where Fk is the force of kinetic friction and N is the normal force. But how do we find N?
Well, my friend, N is basically the weight of the block. And weight is just mass times gravity. So, N = (mass of the block) * (acceleration due to gravity).
Given that the mass of the block is 6.110 kg, and assuming gravity is a flat 9.8 m/s², we can calculate N.
N = 6.110 kg * 9.8 m/s²
Once we have N, we can plug it into our equation to find the force of kinetic friction.
Fk = 0.255 * N
And there you have it! The force of kinetic friction at any time after t = 0 will be equal to 0.255 times the weight of the block.
That's the scoop on the force of friction at different times. Now, go impress your friends with your physics prowess!
To determine the force of friction applied to the block by the table at different times, we need to consider whether the block is moving or not.
1. At time t = 0:
- The applied force F = 16.8 N is greater than the maximum static friction force.
- Therefore, the block will start to move in the direction of the applied force.
- The force of friction applied by the table will still be the maximum static friction force, denoted as Fstatic_max.
2. After the block starts moving:
- Once the block is in motion, the force of friction applied by the table will be the kinetic friction force, denoted as Fkinetic.
- The force of kinetic friction is given by Fkinetic = μk * N, where N is the normal force between the block and the table.
- The normal force N can be calculated as N = m * g, where m is the mass of the block and g is the acceleration due to gravity.
Let's calculate the force of friction applied to the block by the table at the given times using the above information:
1. At time t = 0:
- In this case, the block is not moving.
- The maximum static friction force, Fstatic_max, can be calculated as Fstatic_max = μs * N.
- N = m * g = 6.110 kg * 9.8 m/s² (using the value of acceleration due to gravity).
- Calculate N.
- Calculate Fstatic_max using the given value of μs.
2. After the block starts moving:
- Once the block is in motion, the force of friction applied by the table will be the kinetic friction force, Fkinetic = μk * N.
- Calculate N using the same method as explained before.
- Calculate Fkinetic using the given value of μk.
Let's calculate the values step-by-step. Please provide the value of acceleration due to gravity (g) to proceed.
To determine the force of friction applied to the block by the table at different times, we need to consider two cases: static friction and kinetic friction.
1. Static Friction:
When the block is at rest (before it starts moving), the force of friction is static friction. The magnitude of the static friction force (Fs) can be calculated using the formula:
Fs = μs * N
where μs is the coefficient of static friction and N is the normal force.
The normal force (N) on the block is equal to the weight of the block (mg), where m is the mass of the block and g is the acceleration due to gravity (9.8 m/s^2).
Given:
m = 6.110 kg (mass of the block)
g = 9.8 m/s^2 (acceleration due to gravity)
μs = 0.455 (coefficient of static friction)
First, calculate the normal force N:
N = mg
N = 6.110 kg * 9.8 m/s^2
Next, calculate the force of static friction Fs:
Fs = μs * N
Fs = 0.455 * (6.110 kg * 9.8 m/s^2)
This will give you the force of friction applied to the block by the table when the block is at rest.
2. Kinetic Friction:
Once the block starts moving, the force of friction changes from static friction to kinetic friction. The magnitude of the kinetic friction force (Fk) can be calculated using the formula:
Fk = μk * N
where μk is the coefficient of kinetic friction and N is the normal force.
Using the same normal force value N calculated above, you can calculate the force of kinetic friction Fk:
Fk = μk * N
Fk = 0.255 * (6.110 kg * 9.8 m/s^2)
This will give you the force of friction applied to the block by the table when the block is in motion.
By plugging in the values for mass, gravity, and the coefficients of friction into the formulas provided, you can calculate the force of friction applied to the block by the table at any given time.
At time t = 0: The force of friction applied to the block by the table is 7.6 N (Ff = μs * F = 0.455 * 16.8 = 7.6 N).
At time t = 1 second: The force of friction applied to the block by the table is 6.2 N (Ff = μk * F = 0.255 * 16.8 = 6.2 N).