Hello
given that I person 65 kg takes 4.5 s to climb a flight of stairs that is 5.5 m
my question is well I was asked to solve for the work and
W=fd
and in this case f is equal to the normal force correct? Just take the opposite of mg???????
Also I'm asked to solve for PE and sense PE also equal mgh...
is PE the same as work in this situation????
a similar problem a person is running forwards on a flat surface or 5 m long with a mass of 65 kg and takes 1.75 s starting from rest
I'm asked to solve for the work done
sense F=ma
how do I find the acceleration???
My last question
I'm given a spring that has a mass of 100 g and a constant of 22 N/m with an A of 5 cm
I belive the A is amplitude
and I'm asked for the Total Energy which i don't know how to do
the max velocity also have no idea how to do
and the max force which i don't know how to do
THANK You
As for the stair problem, you have the right idea. The work, mgh, goes into increasing the potential energy.
accelerates starting from rest
d = (1/2) a t^2
5 meters = (1/2) a (1.75)^2
solve for a, the acceleration
m = 100 grams = .1 kg
k = 22 N/m
A = 5 cm = .05 m
y = .05 sin w t
w = sqrt (k/m)
you could solve for w
then maximum stretch = .05 m and velocity is zero there so
Maximum potential energy = maximum energy = (1/2) k .05^2 (This is because the kinetic energy and velocity are zero when the spring is stretched maximum)
Max force = k A
to get maximum velocity
(1/2) m v^2 = max kinetic energy = max total energy = max potential energy which we know
Thank You
Hello!
Let's break down your questions step by step and explain how to solve them:
1. For the person climbing the stairs, you are correct that the work done (W) is equal to the force (f) multiplied by the distance (d) traveled. In this case, the force you need to consider is the normal force (Fn) exerted by the person against gravity. The opposite of the person's weight can be used to find the normal force since it counteracts the force of gravity. So, f = -mg, where m is the mass of the person (65 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). The distance climbed (d) is given as 5.5 m. Therefore, you can calculate the work done (W) as W = f × d.
To calculate the potential energy (PE), you are correct that it is given by the equation PE = mgh. In this case, h represents the vertical height climbed, which is equal to the distance (d) climbed. Therefore, you can use the equation PE = mgh to find the potential energy.
2. For the person running on a flat surface, you are asked to find the work done. The equation for work (W) is still W = fd, where f represents the force applied and d represents the distance covered. In this case, you are not given the force directly, but you can use Newton's second law to find it.
Newton's second law states that force (f) is equal to mass (m) multiplied by acceleration (a), or f = ma. You are given the mass of the person (65 kg). However, you need to find the acceleration. To do that, you can use the equation for average acceleration, which is a = Δv / Δt. Here, Δv represents the change in velocity and Δt represents the change in time. Since the person starts from rest, the initial velocity (u) is 0. The final velocity (v) can be found using the equation v = (d / t), where d is 5 m (the distance covered) and t is 1.75 s (the time taken). Once you have the final velocity, you can use it to calculate the acceleration (a). Finally, with the mass (m) and acceleration (a) known, you can find the force (f) using the equation f = ma. Then, you can find the work done (W) using W = fd.
3. For the spring problem, let's address the different parts individually:
a) Total Energy: The total energy of the spring consists of the potential energy (PE) and the kinetic energy (KE). Given that the spring's mass is 100 g (0.1 kg) and the amplitude (A) of its oscillation is 5 cm (0.05 m), you can calculate the potential energy using PE = (1/2)kA^2, where k is the spring constant (22 N/m) and A is the amplitude. The kinetic energy of the oscillating spring is given by KE = (1/2)mv^2, where m is the mass of the spring and v is the velocity of the mass at any point during oscillation. To find the total energy, simply sum the potential energy and kinetic energy.
b) Maximum Velocity: The maximum velocity (v) of the oscillating mass can be found using the equation v = ωA, where ω represents the angular frequency and is given by ω = sqrt(k/m), where k is the spring constant and m is the mass of the spring.
c) Maximum Force: The maximum force (F) exerted by the spring can be found using Hooke's Law, which states that F = kA, where k is the spring constant and A is the amplitude of the spring's oscillation.
I hope this helps! Let me know if you have any further questions.