A 2000 kg sport car in Figure Q2 (b) accelerates at 6 m/s2 starting from rest. The drag resistance on the car due to the wind is FD = (10 v)N, where v is the velocity in m/s. The running efficiency of the engine is ε = 0.66. Determine the power supplied by the engine when t = 5 s. (8 marks) Figure Q2 (b)
A force vector points at an angle of 61.4∘ above the +x axis. It has a y component of +153 newtons (N). Find (a) the magnitude and (b) the x component of the force vector. (a) Number Units (b) Number Units
A 4.0−kg block is fastened to a spring with spring constant 100 N/m and is oscillating horizontally on a frictionless tabletop with an amplitude of 0.16 m. a) Draw the free-body diagram for the block when its displacement from equilibrium (distance from the center) is 0.12 m. Label all of the forces. b) Use Newton's second law to find the acceleration of the block at this point. c) What is the total mechanical energy of the oscillating block (potential plus kinetic)? Explain your answer.
As shown in the figure, a straight conductor parallel to the "x" axis can slide without friction on the top of two horizontal conducting rails which are parallel to the "y" axis, and at a distance of L = 0.2 m apart, in a magnetic field of magnitude B = 1.5 T and direction -z. A current I = 20 A flows through the conductor in the direction shown. A string is tied exactly at the center of the conductor, passes over a frictionless pulley, having tied at the other end a mass " m " which is suspended vertically. a) Draw the free body diagram of the conductor b) Calculate the magnetic force vector on the conductor c) If the driver is at rest, calculate the mass m in grams
An electron accelerated from rest through potential difference V1 = 5 kV enters the gap between two parallel plates having separation d = 40 mm and potential difference V2 = 100 V. The lower plate is at lower potential. Assume the electric field between the plates is uniform and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. a. What is the direction of the uniform magnetic field (in unit of miliTesla) that allows the electron to travel in a straight line in the gap? (choose 1 for x direction, -1 for negative x direction, ±2 for ±y direction and ±3 for ±z direction.) b. What is the magnitude of this magnetic field (in units of mili-Tesla)?
The bent wire shown in the drawing lies in a uniform magnetic field. Each straight section is 7 m long and makes an angle of θ = 50∘ with the x axis, and the wire carries a current of I = 1.5 A. What is the magnitude of the net magnetic force on the wire if the magnetic field is given by: a. (5 T)z^ b. (5 T)x^
In a magnetic field, a wire moving into the page at v = 10 m/s produces an induced voltage of: Select one: a. 2.5 V to bottom b. zero c. 2.5 V to top d. 2.5 V to left e. 10 V to right
Three point charges are arranged as shown in the figure below. (Take q1 = 5.70 nC, q2 = 4.60 nC, and q3 = −2.82 nC.) (a) Find the magnitude of the electric force on the particle at the origin. N (b) Find the direction of the electric force on the particle at the origin. (counterclockwise from the +x-axis)
Electric charge is distributed over the triangular region D shown below so that the charge density at (x, y) is σ(x, y) = 3xy, measured in coulumbs per square meter (C/m2). Find the total charge on D coulumbs
The tension in a string is 20.2 N, and its linear density is 0.915 kg/m. A wave on the string travels toward the −x direction; it has an amplitude of 3.63 cm and a frequency of 13.0 Hz. What are the (a) speed and (b) wavelength (in terms of m) of the wave? (c) Write down a mathematical expression (like Equation 16.3 or 16.4) for the wave, substituting numbers for the variables A, f, and λ. (a) Number i Units (b) Number Units (c) y = sin(*t ∗x)
A disabled automobile is pulled by means of two ropes as shown. The tension in rope AB is 1.200 kN, and the angle α is 25∘. The resultant of the two forces applied at A is directed along the axis of the automobile. Using trigonometry, determine the tension in rope AC. (Round the final answer to three decimal places.) The tension in the rope AC is kN.
At time 14 s, a car with mass 1000 kg is located at < 106, 0, 20 > m and has momentum < 6000, 0, −3800 > kg⋅m/s. The car's momentum is not changing. At time t2 = 18 s, what is the position of the car? < > m
The three objects shown in the figure above have masses given byA: 240. g B: 130. g C: 280. g. They are connected by massless, rigid rods. What are the coordinates of the centre of mass? (6.00 cm, 2.67 cm) (7.38 cm, 2.95 cm) (5.00 cm, 5.00 cm) (4.80 cm, 1.92 cm)
The three objects shown in the figure above have masses given byA: 220. g B: 320. g C: 60.0 g. They are connected by massless, rigid rods. Find the moment of inertia about an axis that passes through mass B and is perpendicular to the page. 0.0633 kgm2 0.00280 kgm2 0.0280 kgm2 0.00600 kgm2
Three identical point charges, each of mass m = 0.120 kg, hang from three strings, as shown in the figure below. If the lengths of the left and right strings are each L = 32.4 cm, and if the angle θ is 45.0∘, determine the value of q. μC
A quarterback is standing on the football field preparing to throw a pass. His receiver is standing 21 yd down the field and 16 yd to the quarterback's left. The quarterback throws the ball at a velocity of 51 mph toward the receiver at an upward angle of 35∘. Write the initial velocity vector of the ball, v→, in component form. v→ = (Round your answer to 1 decimal place)
For the vectors a→ = (3.0 m)i^ + (4.0 m)j^ and b→ = (5.0 m)i^ + (−2.0 m)j^, give a→+b→ in (a) unit-vector notation, and as (b) a magnitude and (c) an angle (relative to i^ in the range of (−180∘, 180∘)). Now give b→ − a→ in (d) unit-vector notation, and as (e) a magnitude and (f) an angle (relative to i^ in the range of (−180∘, 180∘) (a) Number i^ + j^ Units (b) Number Units (c) Number Units (d) Number i^ + j^ Units (e) Number Units (f) Number Units
(a) In unit-vector notation, what is the sum of a→ = (3.5 m)i^ + (2.8 m)j^ and b→ = (−14.0 m)i^ + (8.3 m)j^. What are (b) the magnitude and (c) the direction of a→ + b→ (relative to i^)? (a) Number i^ + j^ Units (b) Number Units (c) Number Units
A ball accelerates from rest down an inclined plane in two experiments (the acceleration is constant). In the first experiment, its position in units of cm after 2 seconds is marked on the drawing to the left (Fiqure 1). What is the ball's position at t = 3 sec?
A quarterback is standing on the football field preparing to throw a pass. His receiver is standing 22 yd down the field and 13 yd to the quarterback's left. The quarterback throws the ball at a velocity of 70 mph toward the receiver at an upward angle of 35∘. Write the initial velocity vector of the ball, v→, in component form. v→ = (Round your answer to 1 decimal place)
A ball is shot from the ground into the air. At a height of 8.2 m, its velocity is v→ = 7.4i^ + 5.9j^ m/s, with i^ horizontal and j^ upward. (a) To what maximum height does the ball rise? (b) What total horizontal distance does the ball travel? What are the (c) magnitude and (d) angle (below the horizontal; give as negative) of the ball's velocity just before it hits the ground? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A ball A is moving with a speed of 2 m/s at a 45∘ angle and collides with a stationary ball B. The balls are identical in mass and size, and the coefficient of restitution between the balls is e = 0.9. Determine the velocities of the balls after the collision and the direction of ball A(vA′, vB′, θ).
The bike is moving along a straight road with the speed described by the v-s graph. Construct the a-s graph of the motion and determine the time needed for the motorcycle to reach the position s = 525 m.
A mass spectrometer is a device like the one shown in the attached figure. A particle with a total charge q = 4.8⋆10^-19 [C] is directed with a velocity of magnitude v = 4.5⋆10∧6[m/s] in a space where there is a uniform magnetic field of magnitude B = 0.8⋆10^-4 [T] describing a circular orbit of radius r = 1.2 [m]. Determine the mass v m of the particle in kg.
As you will see in a later chapter, forces are vector quantities, and the total force on an object is the vector sum of all forces acting on it. In the figure below, a force F→1 of magnitude 6.40 units acts on a crate at the origin in a direction θ = 27.0∘ above the positive x-axis. A second force F→2 of magnitude 5.00 units acts on the crate in the direction of the positive y-axis. Find graphically the magnitude and direction (in degrees counterclockwise from the +x-axis) of the resultant force F→1 + F→2 magnitude units direction counterclockwise from the +x-axis
Let P be a point not on the line L that passes through the points Q and R. The distance d from the point P to the line L is d = |a×b| |a| where a = QR→ and b = QP→ Use the above formula to find the distance from the point to the given line. d =
What is the electric field at a location b→ = ⟨-0.5, -0.2, 0⟩m, due to a particle with charge +1 nC located at the origin? E→ =
The figure below shows a 108 -turn square coil rotating about a vertical axis at at ω = 1,580 rev/min. The length of a side of the coil is 20.0 cm. The horizontal component of the Earth's magnetic field at the coil's location is equal to 2.00×10−5 T. (a) What is the magnitude of the maximum emf (in mV) induced in the coil by the Earth's magnetic field? mV (b) What is the orientation of the coil with respect to the magnetic field when the maximum emf occurs? The plane of the coil is oriented 45∘ with respect to the magnetic field. The plane of the coil is parallel to the magnetic field. The plane of the coil is perpendicular to the magnetic field.
Car A is travelling along a straight line with a velocity of 100 km/h. Car B travels at a speed of 50 km/h along a circular path with a radius of curvature of 20 m. As shown in Figure Q3, the speed of car A is increasing at a rate of 20 km/h2 and the speed of car B is reducing at a rate of 10 km/h2. Fig. Q3 Diagram of the two-car problem. (i) Determine the velocity of the car B as measured by the observer A. [5 marks] (ii) Determine the acceleration of the car B as measured by the observer A. [5 marks] (iii) Determine the velocity of the car A as measured by the observer B. [5 marks] (iv) Determine the acceleration of the car A as measured by the observer B. [5 marks]
In traveling a distance of 4.9 km between points A and D, a car is driven at 115 km/h from A to B for t seconds and 61 km/h from C to D also for t seconds. If the brakes are applied for 5.1 seconds between B and C to give the car a uniform deceleration, calculate t and the distance s between A and B. Answers: t = s S = km
An automobile traveling 54.0 km/h has tires of 72.0 cm diameter. (a) What is the angular speed of the tires about their axles? (b) If the car is brought to a stop uniformly in 29.0 complete turns of the tires, what is the magnitude of the angular acceleration of the wheels? (c) How far does the car move during the braking? (Note: automobile moves without sliding) (a) Number Units (b) Number Units (c) Number Units
A train at a constant 42.0 km/h moves east for 24.0 min, then in a direction 51.0∘ east of due north for 29.0 min, and then west for 34.0 min. What are the (a) magnitude and (b) angle (relative to east) of its average velocity during this trip? (a) Number Units (b) Number Units
A car with mass of 1500 kg is traveling at 80 km/h. The brakes are fully applied at this moment, resulting in wheel skidding. The road conditions are for two scenarios: (a) on dry pavement with a coefficient of kinetic friction μk = 0.8; and (b) on icy road with a coefficient of kinetic friction μk = 0.1. Assume gravity g = 9.81 m/s2. Show all work. a) Draw the appropriate free body and kinetic diagram(s). (2 points) b) Write the equations of motion based on the free body and kinetic diagram(s) written above. (2 points) c) Compute the expression of deceleration, a, in terms of μk. (2 points) d) Determine the magnitude of deceleration on dry pavement, adry. (2 points) e) Determine the stopping time on dry pavement, tdry. (2 points) f) Determine the magnitude of deceleration on icy road, aicy. (2 points) g) Determine the stopping time on icy road, ticy. . (2 points) →80 km/h
A 6.62−kg piece of copper metal is heated from 18.5∘C to 328.3∘C. Calculate the heat absorbed (in kJ) by the metal. The specific heat of copper is 0.385 J/g⋅∘C. kJ (Enter your answer in scientific notation.)
A car travels 21 km east and then 26 km north in 59 minutes. Take i^ to represent a unit vector in the easterly direction and j^ to represent a unit vector in the northerly direction. Give your answer with the correct number of significant figures. Part 1) What is the displacement of the car? i^ + j^ m Part 2) What is the average speed of the car? km/h Part 3) What is the average velocity of the car? i^ + j^ km/h
A 44.4−kg girl is standing on a 141-kg plank. Both originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity of 1.58 im/s relative to the plank. (a) What is the velocity of the plank relative to the ice surface? î m/s (b) What is the girl's velocity relative to the ice surface? i^ m/s
The graph of the velocity (in km/h) of a car that is accelerating is shown in the figure, where t is measured in seconds. (a) Use the midpoint rule with n = 3 to estimate the average velocity vave (in km/h) of the car during the first 12 seconds. vave = km/h (b) At what time t (in s) was the instantaneous velocity equal to the average velocity? (Round your answer to one decimal place.) t = s
2/42 Car A travels at a constant speed of 100 km/h. When in the position shown at time t = 0, car B has a speed of 40 km/h and accelerates at a constant rate of 0.1 g along its path until it reaches a speed of 100 km/h, after which it travels at that constant speed. What is the steady-state position of carA with respect to car B? PROBLEM 2/42
An airplane is flying in a horizontal circle at a speed of 420 km/h (see the figure). If its wings are tilted at angle θ = 42.0∘ to the horizontal, what is the radius of the circle in which the plane is flying? Assume that the required force is provided entirely by an "aerodynamic lift" that is perpendicular to the wing surface. Number Units
A student drove to the university from her home and noted that the odometer reading of her car increased by 16.0 km. The trip took 19.0 min. (a) What was her average speed in km/h? km/h (b) If the straight-line distance from her home to the university is 10.3 km in a direction 25.0∘ south of east, what was her average velocity in km/h? km/h (c) If she returned home by the same path 7 h 30 min after she left, what were her average speed and velocity in km/h for the entire trip? average speed km/h average velocity km/h
A boat is traveling upstream at 10 km/h with respect to the water of a river. The water is flowing at 5.0 km/h with respect to the ground. What are the (a) magnitude and (b) direction of the boat's velocity with respect to the ground? A child on the boat walks from front to rear at 6.0 km/h with respect to the boat. What are the (c) magnitude and (d) direction of the child's velocity with respect to the ground? (a) Number Units (b) (c) Number Units (d)
A skateboarder shoots off a ramp with a velocity of 7.4 m/s, directed at an angle of 51∘ above the horizontal. The end of the ramp is 1.2 m above the ground. Let the x axis be parallel to the ground, the +y direction be vertically upward, and take as the origin the point on the ground directly below the top of the ramp. (a) How high above the ground is the highest point that the skateboarder reaches? (b) When the skateboarder reaches the highest point, how far is this point horizontally from the end of the ramp? (a) Number Units (b) Number Units
A small island is a = 3 km away from the nearest point P on the straight shoreline of a large lake. A town is b = 12 km down the shore from P as shown in the figure below. If a person on the island can row a boat 2.8 km/h and can walk 5 km/h, where should the boat be landed (xkm from the point P) so that the person arrives in the town in the shortest time? (Use decimal notation. Give your answer to three decimal places.) Recall: The distance formula is: d = r⋅t and can also be written as: t = dr Check the "Student Hint", if you would like further help with the set up of this question. x = km
Person A is 10 km south of person B. A walks north at a speed of 2 km/h. B walks east at a speed of 3 km/h. If they both start at 2:00 p.m., determine the closest distance they will ever be from each other and the time this occurs. Draw on the diagram to support your opening equation. [8 marks]