FIGURE EX shows the velocity graph of a kg passenger in an elevator. What is the passenger’s weight
a. At s?
b. At s?
c. At s?
a. The passenger weight at is
b. The passenger weight at is
c. The passenger weight at is
Weight of an object is the gravitational force exerted on it and it is the product of the mass of the object m and the gravitational acceleration g.
The equation for the apparent weight of the passenger is
Here, a is acceleration of the passenger.
The expression which relates acceleration, velocity and time is
The acceleration of passengers between time is
The acceleration of passenger at is zero.
The equation for apparent weight of the passenger at time is
The acceleration of passenger at is
The equation for apparent weight of the passenger at time
A block of mass is at rest at the origin at . It is pushed with constant force from to across a horizontal surface whose coefficient of kinetic friction is . That is, the coefficient of friction decreases from at to zero at .
a. Use what you've learned in calculus to prove that
b. Find an expression for the block's speed as it reaches position .
You're driving along at with your aunt's valuable antiques in the back of your pickup truck when suddenly you see a giant hole in the road ahead of you. Fortunately, your foot is right beside the brake and your reaction time is zero!
a. Can you stop the truck before it falls into the hole?
b. If your answer to part a is yes, can you stop without the antiques sliding and being damaged? Their coefficients of friction are and .
A spring-loaded toy gun exerts a variable force on a plastic ball as the spring expands. Consider a horizontal spring and a ball of mass m whose position when barely touching a fully expanded spring is . The ball is pushed to the left, compressing the spring. You’ll learn in Chapter that the spring force on the ball, when the ball is at position (which is negative), can be written as , where k is called the spring constant. The minus sign is needed to make the -component of the force positive. Suppose the ball is initially pushed to , then released and shot to the right.
a. Use what you’ve learned in calculus to prove that
b. Find an expression, in terms of , , and , for the speed of the ball as it comes off the spring at .
Very small objects, such as dust particles, experience a linear drag force, (bv, direction opposite the motion), where is a constant. That is, the quadratic model of drag of Equation fails for very small particles. For a sphere of radius , the drag constant can be shown to be , where is the viscosity of the gas.
a. Find an expression for the terminal speed of a spherical particle of radius and mass falling through a gas of viscosity .
b. Suppose a gust of wind has carried a -diameter dust particle to a height of . If the wind suddenly stops, how long will it take the dust particle to settle back to the ground? Dust has a density of the viscosity of air is , and you can assume that the falling dust particle reaches terminal speed almost instantly.
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