1.) A 7159 N piano is to be pushed up a(n) 2.26 m
frictionless plank that makes an angle of 25.6 degrees with the horizontal.
Calculate the work done in sliding the piano
up the plank at a slow constant rate.
Answer in units of J.
2.) A 20 g bullet is accelerated in a rifle barrel
45 cm long to a speed of 354 m/s.
Use the work-energy theorem to find the
average force exerted on the bullet while it is
being accelerated.
Answer in units of N.
3.) A 4.17 g bullet moving at 506.1 m/s penetrates
a tree trunk to a depth of 4.64 cm.
Use work and energy considerations to
find the magnitude of the force that stops the
bullet.
Answer in units of N.
posted these already but the answers were marked incorrect
1. To answer this you use the formula W=fd, you have the force because the piano is moving at a slow constant rate so its overcoming its gravity in the X direction, so you can find F and 2.26M is your Displacement (D)
i don't know how to do than the last person who answered tried it but it involved sin and calculus stuff like that
1. M*g = 7159 N.
M = 7159/g = 7159/9.8 = 731 kg.
Fp = 7159*sin25.6 = 3093 N. = Force parallel to the plank.
Fap-Fp = M*a.
Fap - 3093 = M*0 = 0.
Fap = 3093 N. = Force applied.
Work = Fap*d = 3093 * 2.26 = 6991 J.
2. Work = KE2-KE1 = 0.5M*V^2- 0 = 0.5*0.02*354^2 = 1253 J.
To solve these questions, we need to apply the concepts of work and energy. The work done is given by the formula:
Work = Force x Displacement x cos(θ)
Where:
- Force is the applied force on the object,
- Displacement is the distance the object is moved,
- θ is the angle between the applied force and the direction of displacement.
Now, let's solve each question step by step:
1.) To calculate the work done in sliding the piano up the plank, we need to find the component of the weight force parallel to the direction of displacement.
The component of the weight force parallel to the direction of displacement is given by:
Force_parallel = Weight x sin(θ)
Force_parallel = 7159 N x sin(25.6°)
The displacement is given as 2.26 m, and the angle is given as 25.6°.
Now, we can substitute these values into the formula for work:
Work = Force_parallel x Displacement x cos(θ)
Calculate the numerical answer using the given values and the formula for work.
2.) In this question, we need to find the average force exerted on the bullet as it is accelerated in the rifle barrel.
According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be written as:
Work = ΔKinetic Energy
Work = (1/2)mv²
Here, m is the mass of the bullet (20 g), and v is the velocity of the bullet (354 m/s).
We know the work done on the bullet, and we need to find the average force. Use the formula for work to calculate the numerical answer.
3.) In this question, we need to find the magnitude of the force that stops the bullet as it penetrates the tree trunk.
The work done on the bullet can be written as:
Work = Force x Displacement
Here, the displacement is given as 4.64 cm (which needs to be converted to meters), and we need to find the force.
Since we know the work done on the bullet, we can use the formula to calculate the numerical answer.
Remember to perform the necessary unit conversions and use appropriate values in the formulas to get accurate answers.